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Thread: coin flipped

  1. #1
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    coin flipped

    the probability of getting a head on flipping a biased coin is p. the coin is flipped n times producing a sequence containing m heads and (n-m) tails what is the probability of obtaining this sequence from n flips.
    i cant understand the wording
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  2. #2
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    Re: coin flipped

    You have a biased coin with probability of flipping heads = $p$

    You flip this coin $n$ times

    what is the probability you flip $m$ heads
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    Re: coin flipped

    Is it P(n)^m
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    Re: coin flipped

    Is it P(n)^m
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    Re: coin flipped

    Have you studied the binomial distribution yet?
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    Re: coin flipped

    yes
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    Re: coin flipped

    Quote Originally Posted by markosheehan View Post
    yes
    Ok. So you should be familiar with the formula:

    P(X=r) = nCr*p^r*q^{n-r}

    So, what is n, r, p and q in this case?
    Last edited by Debsta; Jan 3rd 2017 at 12:08 PM.
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  8. #8
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    Re: coin flipped

    when i put this all together i get (n ncr m)*p*(1-p)^n-m however at the back of the book it says the answer is p^m(1-p)^n-m
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    Re: coin flipped

    Quote Originally Posted by markosheehan View Post
    when i put this all together i get (n ncr m)*p*(1-p)^n-m however at the back of the book it says the answer is p^m(1-p)^n-m
    Did you mean p^m rather than just p in your answer?

    Going back to the question "the coin is flipped n times producing a sequence containing m heads and (n-m) tails". If this means "m heads and then (n-m) tails",
    the answer in your book is correct. The nCm multiplier accounts for all the ways you can get m heads and (n-m) tails , ie in any order.

    I would interpret "a sequence containing m heads and (n-m) tails" as meaning "in any order" eg HHHTT, HTHTH, THHHT all need to be accounted for.

    I stick by my answer.
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